Solve 16ab^2x^3/-4ab^2x=

$$\frac { 16 a b ^ { 2 } x ^ { 3 } } { - 4 a b ^ { 2 } x } =$$

Evaluate

$$-4x^{2}$$

Solution Steps

Cancel out 4axb^{2} in both numerator and denominator.

$$\frac{4x^{2}}{-1}$$

Anything divided by -1 gives its opposite.

$$-4x^{2}$$

Differentiate w.r.t. x

$$-8x$$

Steps Using Definition of a Derivative

Cancel out 4axb^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4x^{2}}{-1})$$

Anything divided by -1 gives its opposite.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4x^{2})$$

The derivative of ax^{n} is nax^{n-1}.

$$2\left(-4\right)x^{2-1}$$

Multiply 2 times -4.

$$-8x^{2-1}$$

Subtract 1 from 2.

$$-8x^{1}$$

For any term t, t^{1}=t.

$$-8x$$